I don't think the 1st to move Monahan was just so that they could sign Kadri. It also leaves them with a cap cushion of $300k-$600k or so if they run a 23 man roster (more if they run 22 guys for stretches to bank cap space). They should wind up with enough banked space to bring in a good rental at the deadline if they want to go that route.
They probably could have paid less to fit Kadri in, but wouldn't have had mid-season cap flexibility without a season ending injury. I think the 1st is better described as being moved to sign Kadri and still be able to get a deadline rental. Still not great in a vacuum, but not terrible.
But balanced against the rest of their summer, I think it makes a lot more sense. The 1st rounder is going to be in 2024-2026 and is going to be a mid-to-late 1st rounder depending on conditions. The 2025 (or maybe 2026) 1st rounder they got in the Tkachuk deal is what made that asset expendable and it very well might be the actual pick sent to Montreal. I'd still have been praising them for the Tkachuk trade if they had sent off Monahan in the deal instead of getting Florida's 1st rounder. If the Tkachuk deal had been a 3 way trade where Montreal got Monahan and Florida's 1st, absolutely no one would have criticized Calgary. The pick they wound up sending Montreal is slightly better than that (the conditions make it fairly likely that Montreal will get one of their picks instead), but the bones of the deal are the same.
Calgary did not get more expensive in the short term. They were above the cap last year and needed Monahan on LTIR to field a compliant roster. They currently have $2.1M in space and will be a bit under the cap if/when they add 2 guys to the roster. And the 'replacements' for Gaudreau and Tkachuk are much cheaper right now. Huberdeau, Kadri, and Weegar cost $3M less than what Gaudreau and Tkachuk cost this year. Even if Gaudreau/Tkachuk had been willing to stay, Calgary would have needed to trade Monahan and clear another few million to fit them. Huberdeau gets more expensive in 2023/24, but him and Kadri will still be making a couple million less than Gaudreau and Tkachuk. With Lucic coming off the books, they can afford a Weegar extension if he is willing to sign.
Again, I'm happy the Blues didn't sign this contract and I think there is a good chance that Kadri underperforms the AAV every year. But in the first few years he shouldn't underperform the AAV by much and should be a good contributor for them. Turning two studs who clearly weren't coming back and a Monahan dump into Huberdeau/Kadri long term at $17.5M and 1 year of Weegar is just not a terrible summer.